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Prior to 1959 both the IUPAP and IUPAC used oxygen to define the mole; the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/60 to define the mole as follows.

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

The Hoyle state is an excited, spinless, resonant state of carbon-12. It is produced via the triple-alpha process, and was predicted to exist by Fred Hoyle in 1954.[2] The existence of the Hoyle state is essential for the nucleosynthesis of carbon in helium-burning red giant stars, and predicts an amount of carbon production in a stellar environment which matches observations. The existence of the Hoyle state has been confirmed experimentally, but its precise properties are still being investigated.[3] In 2011, an ab initio calculation of the low-lying states of carbon-12 found (in addition to the ground and excited spin-2 state) a resonance with all of the properties of the Hoyle state.[4][5]